oceanography
| Green G and Fleischmann R (2019), "Branched flow and caustics in nonlinear waves", New Journal of Physics., August, 2019. Vol. 21(8), pp. 083020. |
| Abstract: Rogue waves, i.e. high amplitude fluctuations in random wave fields, have been studied in several contexts, ranging from optics via acoustics to the propagation of ocean waves. Scattering by disorder, like current fields and wind fluctuations in the ocean, as well as nonlinearities in the wave equations provide widely studied mechanisms for their creation. However, the interaction of these mechanisms is largely unexplored. Hence, we study wave propagation under the concurrent influence of geometrical (disorder) and nonlinear focusing in the (current-modified) nonlinear Schrödinger equation. We show how nonlinearity shifts the onset distance of geometrical (disorder) focusing and alters the peak intensities of the fluctuations. We find an intricate interplay of both mechanisms that is reflected in the observation of optimal ratios of nonlinearity and disorder strength for the generation of rogue waves. |
BibTeX:
@article{green_branched_2019,
author = {Green, Gerrit and Fleischmann, Ragnar},
title = {Branched flow and caustics in nonlinear waves},
journal = {New Journal of Physics},
year = {2019},
volume = {21},
number = {8},
pages = {083020},
doi = {10.1088/1367-2630/ab319b}
}
|
| Degueldre H, Metzger JJ, Geisel T and Fleischmann R (2016), "Random focusing of tsunami waves", Nature Physics., March, 2016. Vol. 12(3), pp. 259-262. |
| Abstract: Tsunamis exhibit surprisingly strong height fluctuations. An in-depth understanding of the mechanisms that lead to these variations in wave height is a prerequisite for reliable tsunami forecasting. It is known, for example, that the presence of large underwater islands or the shape of the tsunami source can affect the wave heights. Here we show that the consecutive effect of even tiny fluctuations in the profile of the ocean floor (the bathymetry) can cause unexpectedly strong fluctuations in the wave height of tsunamis, with maxima several times higher than the average wave height. A novel approach combining stochastic caustic theory and shallow water wave dynamics allows us to determine the typical propagation distance at which the strongly focused waves appear. We demonstrate that owing to this mechanism the small errors present in bathymetry measurements can lead to drastic variations in predicted tsunami heights. Our results show that a precise knowledge of the ocean’s bathymetry is absolutely indispensable for reliable tsunami forecasts. |
BibTeX:
@article{degueldre_random_2016,
author = {Degueldre, Henri and Metzger, Jakob J. and Geisel, Theo and Fleischmann, Ragnar},
title = {Random focusing of tsunami waves},
journal = {Nature Physics},
year = {2016},
volume = {12},
number = {3},
pages = {259--262},
url = {http://www.nature.com/nphys/journal/v12/n3/full/nphys3557.html},
doi = {10.1038/nphys3557}
}
|
| Kanoglu U, Titov VV, Aydin B, Moore C, Stefanakis TS, Zhou H, Spillane M and Synolakis CE (2013), "Focusing of long waves with finite crest over constant depth", Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences., February, 2013. Vol. 469(2153), pp. 20130015-20130015. |
BibTeX:
@article{Kanoglu2013,
author = {Kanoglu, U. and Titov, V. V. and Aydin, B. and Moore, C. and Stefanakis, T. S. and Zhou, H. and Spillane, M. and Synolakis, C. E.},
title = {Focusing of long waves with finite crest over constant depth},
journal = {Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences},
year = {2013},
volume = {469},
number = {2153},
pages = {20130015--20130015},
doi = {10.1098/rspa.2013.0015}
}
|
| Ying L and Kaplan L (2012), "Systematic study of rogue wave probability distributions in a fourth-order nonlinear Schrödinger equation", Journal of Geophysical Research C: Oceans. Vol. 117(8) |
| Abstract: Nonlinear instability and refraction by ocean currents are both important mechanisms that go beyond the Rayleigh approximation and may be responsible for the formation of freak waves. In this paper, we quantitatively study nonlinear effects on the evolution of surface gravity waves on the ocean, to explore systematically the effects of various input parameters on the probability of freak wave formation. The fourth-order current-modified nonlinear Schrödinger equation (CNLS 4) is employed to describe the wave evolution. By solving CNLS 4 numerically, we are able to obtain quantitative predictions for the wave height distribution as a function of key environmental conditions such as average steepness, angular spread, and frequency spread of the local sea state. Additionally, we explore the spatial dependence of the wave height distribution, associated with the buildup of nonlinear development. ©2012. American Geophysical Union. All Rights Reserved. |
BibTeX:
@article{Ying2012,
author = {Ying, L.H. and Kaplan, L.},
title = {Systematic study of rogue wave probability distributions in a fourth-order nonlinear Schrödinger equation},
journal = {Journal of Geophysical Research C: Oceans},
year = {2012},
volume = {117},
number = {8}
}
|
| Ying LH, Zhuang Z, Heller EJ and Kaplan L (2011), "Linear and nonlinear rogue wave statistics in the presence of random currents", Nonlinearity., November, 2011. Vol. 24(11), pp. R67-R87. |
BibTeX:
@article{Ying2011,
author = {Ying, L H and Zhuang, Z and Heller, E J and Kaplan, L},
title = {Linear and nonlinear rogue wave statistics in the presence of random currents},
journal = {Nonlinearity},
year = {2011},
volume = {24},
number = {11},
pages = {R67--R87},
url = {http://stacks.iop.org/0951-7715/24/i=11/a=R01?key=crossref.fd1d2c5fbe1d7415dd17bea46748e691},
doi = {10.1088/0951-7715/24/11/R01}
}
|
|
Heller EJ, Kaplan L and Dahlen A (2008), "Refraction of a Gaussian seaway", Preprint.
[BibTeX] |
BibTeX:
@article{Heller2008,
author = {Heller, E. J. and Kaplan, L. and Dahlen, A.},
title = {Refraction of a Gaussian seaway},
journal = {Preprint},
year = {2008}
}
|
|
Berry MV (2007), "Focused tsunami waves", Proceedings of the Royal Society A. Vol. 463(2087), pp. 3055.
[BibTeX] |
BibTeX:
@article{Berry2007,
author = {Berry, M. V.},
title = {Focused tsunami waves},
journal = {Proceedings of the Royal Society A},
year = {2007},
volume = {463},
number = {2087},
pages = {3055}
}
|
| Heller E (2005), "Freak waves: just bad luck, or avoidable?", Europhysics News., September, 2005. Vol. 36(5), pp. 159-162. |
BibTeX:
@article{Heller2005,
author = {Heller, Eric},
title = {Freak waves: just bad luck, or avoidable?},
journal = {Europhysics News},
year = {2005},
volume = {36},
number = {5},
pages = {159--162},
doi = {10.1051/epn:2005504}
}
|
|
White BS and Fornberg B (1998), "On the chance of freak waves at sea", Journal of Fluid Mechanics. Vol. 355, pp. 113-138.
[BibTeX] |
BibTeX:
@article{White1998,
author = {White, B. S and Fornberg, B.},
title = {On the chance of freak waves at sea},
journal = {Journal of Fluid Mechanics},
year = {1998},
volume = {355},
pages = {113--138}
}
|
